This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A199675 #14 Feb 16 2025 05:36:09
%S A199675 1,1,2,7,31,170,1129,8737,77198,767683,8482519,103093958,1366897597,
%T A199675 19633740673,303706037546,5033465370031,88983532209967,
%U A199675 1671402633292562,33241154368669921,697834148797749601,15420722865332961206,357805114894717632331,8697446048869287663271
%N A199675 Expansion of e.g.f. 1/(exp(-x) - Sum_{n>=0} (-x)^(3*n+2)/(3*n+2)!).
%F A199675 E.g.f.: A(x) = 1/Q(0); Q(k) = 1-x/((3*k+1)-(x^2)*(3*k+1)/((x^2)+3*(3*k+2)*(k+1)/Q(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Nov 26 2011
%e A199675 E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 31*x^4/4! + 170*x^5/5! +...
%e A199675 where
%e A199675 A(x) = 1/(1 - x - x^3/3! + x^4/4! + x^6/6! - x^7/7! - x^9/9! + x^10/10! +...).
%o A199675 (PARI) {a(n)=n!*polcoeff(1/(exp(-x+x*O(x^n)) - sum(m=0, n\3, (-x)^(3*m+2)/(3*m+2)! )), n)}
%o A199675 (PARI) {a(n)=n!*polcoeff(1/(sum(m=0, n\3+1, (-x)^(3*m)/(3*m)! + (-x)^(3*m+1)/(3*m+1)! +x^2*O(x^n))), n)}
%Y A199675 Cf. A049774, A199670.
%K A199675 nonn
%O A199675 0,3
%A A199675 _Paul D. Hanna_, Nov 09 2011